In relation to an entity, e.g., a business enterprise or a firm, that wants to maximize revenue by providing promotions to its customers, that entity must first decide on which promotion to provide to which customer, and additionally needs to predict the probabilities that the customer accepts each promotion.
However, feature importance in the context of prediction is not necessarily appropriate.
That is, for example, supposing a certain customer “feature” such as customer's age has a strong influence to the likelihood of acceptance for all promotion options including no promotion option: this “feature” is important in predicting customers' acceptance decisions. However, this feature may not be important in determining which promotion to provide if the responses to each promotion is influenced uniformly.
Thus, while literature exists on feature importance (or feature selection) as concerning a feature's influence to the likelihood of acceptance for all promotion options including no promotion, there is no concern for defining importance of features in the context of recommending promotions to maximize a profit.
Thus, it is a challenge how to effectively identify features and their importance in determining not only to which customers promotions (e.g., of products or services) are to be targeted, but to generally identify the key features that are useful to make optimal promotion recommendations to a target population, and automatically provide valuation business insights.